WHEN? The minute QA receives a build from development and before all the team starts deploying it on their testing environments.
WHAT? A 1 to 2 hour intensive test suit that comes to assure the build is good enough for the whole team to commit to it. This is a great candidate for automation (and if so, it can be run each day as part of nightly build system).
WHY? Even after developers perform their Integration Tests it is not always enough for the QA to start testing it. We need to make sure there are no blockers or other stability issues that would prevent you from executing your test plan.